Electrical – What size and type wire should I use to pigtail to the light switches

The wire that "loops" between the two switches is the hot wire from the power source. This is the same as having a single wire with 2 pig tails that connect to each switch. Since you're replacing two single-pole single-throw (SPST) switches with two of the same types, all you need to do is replace them with the exact same wiring that currently exists. There is no hot/neutral to these switches, so as long as you connect to the two screws on each switch, you will be OK.

For the ground, in the pictures you can see the bare ground wires (with some paint on them) with a wire nut at the very back of the electrical box. You can and add in two pig-tails in order to connect to your new switches ground terminals. In your particular case, since you have a plastic electrical box, you should definitely connect this wire. If your box was metal, then the switch would be grounded just by making contact with the electrical box (assuming the box were grounded).

Conduit is a fine way to do it. One of the luxuries of working in conduit is you can install any wires the circuit requires. This is safer too, because it assures that hots and neutrals actually are together. There's no problem with transitioning between cable and conduit of any kind, so long as you are in locations appropriate to both types.

It's also easier to wire, since you aren't stuck with red and black (or marking white or gray neutrals). You can use any color you please; brown, orange, yellow, blue, purple or pink. Even my local lumberyard sells several of those by the foot. Of course green can never be anything but ground, even in a conduit. (thanks gregmac for reminding me to specify what I assume you know, but the next reader might not.)

In metal conduit you must bond the conduit to ground, but you also can let the conduit be the ground, so one less wire to pull. To make a transition from wired ground to conduit ground, the boxes have a hole tapped for 10-32 for attaching the ground wire. For convenience, they sell green screws 10 for a buck, and pre-made ground pigtails 10 for $3.